Optical Glucose Monitoring Based on Femtosecond Two-Color Pulse Interferometry

We demonstrate the potential of femtosecond two-color pulse interferometry for in vitro optical glucose monitoring, by dispersion of the group refractive index in a glucose solution sample with respect to a red-color light and a blue-color light. By comparison with femtosecond one-color pulse interferometry, the basic performance of the present system with regard to sensitivity, quantitativeness, and tolerance to surrounding disturbances, is evaluated. The resulting accuracy and precision of glucose determination are 77 and 118mg/dl for 10-mm-sample-thickness, respectively. This near-common-path configuration of the two-color pulse light provides good stability to fluctuations of sample temperature, which is important in clinical applications. Considering the performance of femtosecond two-color pulse interferometry as an optical glucose sensor, a suitable measurement site for in vivo optical glucose monitoring is discussed.     

A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

We construct a new family of cyclic difference sets with parameters ((3 ^d – 1)/2, (3 ^{d – 1} – 1)/2, (3 ^{d – 2} – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.     

Recognition of the Finite Simple Groups F 4(2m) by Spectrum

The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum, if every finite group with the same spectrum as G is isomorphic to G. The purpose of the paper is to prove that for every natural m the finite simple Chevalley group F ₄(2 ^m ) is recognizable by spectrum.     

代数课程教学改革的一些探索

本文结合代数教学中的实际情况．针对代数教学过程中出现的问题。提出了在代数教学过程中改进教学方法的几条措施．     

The Hopf Property for Subgroups of Hyperbolic Groups

A group is said to be Hopfian if every surjective endomorphism of the group is injective. We show that finitely generated subgroups of torsion-free hyperbolic groups are Hopfian. Our proof generalizes a theorem of Sela (Topology 35 (2) 1999, 301–321).     

Dubrovin赋值斜群环

本文中对一个斜群环为Dubrovin赋值环给出了一系列等价刻画,并且刻画了一个Dubrovin赋值斜群环的所有素理想.     

On Quasiclassical Field Theories Invariant with Respect to a Lie Group

Mathematical Notes -     

SOME SUBGROUPS OF THE EXTENDED HECKE GROUPS (λ_q)

The authors consider the extended Hecke groups H(λq) generated by T(z) = -1 / z, S(z) = -1/(z + λq,) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(λq), the second commutator subgroup H (λq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups H(λq) are studied. Also, relations between them are given.     

Optimal stopping problems by two or more decision makers: a survey

A review of the optimal stopping problem with more than a single decision maker (DM) is presented in this paper. We classify the existing literature according to the arrival of the offers, the utility of the DMs, the length of the sequence of offers, the nature of the game and the number of offers to be selected. We enumerate various definitions for this problem and describe some dynamic approaches. Fouad Ben Abdelaziz is on leave from the Institut Superieur de Gestion, University of Tunis, Tunisia e-mail: foued.benabdelaz@isg.run.tn.     

Mental representations of important real-life decisions

Two studies investigated how decision makers characterize alternatives in important real-life decisions, which they themselves had made (to leave a partner, to choose an education and to choose a home). First, the participants indicated a very high degree of involvement in the decisions studied and about half of the participants gave maximum involvement ratings for the partner decision. Second, the results showed that concepts that are essential in most decision theories, such as, consequence, probability and value were important characteristics of the decisions. Third, emotion, positive and negative affect were also important characteristics. Fourth, value and emotion were uncorrelated. Fifth, the patterns of characteristics of decisions made in the past did not differ markedly from the characteristics given to future decisions. Principal component analyses were performed on the ratings of applicability of the different characteristics across participants for each decision situation. Three factors were extracted. There was one factor for positive affect/emotions and another factor for negative affect/emotions verified in oblique solutions. Thus, different scales are needed to represent emotion/affect components (and not bipolar scales) in real-life important decisions. The third factor represented the way in which a decision was represented (moving pictures dialogue etc.). An analysis restricted to the participants who rated 100% involvement showed an additional fourth factor with “what others would think”, “similar situations”, “values” and “money” as the most prominent characteristics. This points to the importance of controlling for participant involvement in studies of human decision making to enable generalizations to real-life decisions.